Derived from Karhunen-Loeve's transformation. Given an s-dimensional vector representation of each face in a training set of images, Principal Component Analysis (PCA) tends to find a t-dimensional subspace whose basis vectors correspond to the maximum variance direction in the original image space. This new subspace is normally lower dimensional (t<<s). If the image elements are considered as random variables, the PCA basis vectors are defined as eigenvectors of the scatter matrix.

Linear Discriminant Analysis (LDA) finds the vectors in the underlying space that best discriminate among classes. For all samples of all classes the between-class scatter matrix SBand the within-class scatter matrix SW are defined. The goal is to maximize SBwhile minimizing SW, in other words, maximize the ratio det|SB|/det|SW| . This ratio is maximized when the column vectors of the projection matrix are the eigenvectors of (SW^-1 × SB).

An eigenspace-based adaptive approach that searches for the best set of projection axes in order to maximize a fitness function, measuring at the same time the classification accuracy and generalization ability of the system. Because the dimension of the solution space of this problem is too big, it is solved using a specific kind of genetic algorithm called Evolutionary Pursuit (EP).

Elastic Bunch Graph Matching (EBGM). All human faces share a similar topological structure. Faces are represented as graphs, with nodes positioned at fiducial points. (exes, nose...) and edges labeled with 2-D distance vectors. Each node contains a set of 40 complex Gabor wavelet coefficients at different scales and orientations (phase, amplitude). They are called "jets". Recognition is based on labeled graphs. A labeled graph is a set of nodes connected by edges, nodes are labeled with jets, edges are labeled with distances.

The Trace transform, a generalization of the Radon
transform, is a new tool for image processing which can be
used for recognizing objects under transformations, e.g. rotation,
translation and scaling. To produce the Trace transform
one computes a functional along tracing lines of an image.
Different Trace transforms can be produced from an image
using different trace functionals.

An Active Appearance Model (AAM) is an integrated statistical model which combines a model of shape variation with a model of the appearance variations in a shape-normalized frame. An AAM contains a statistical model of the shape and gray-level appearance of the object of interest which can generalize to almost any valid example. Matching to an image involves finding model parameters which minimize the difference between the image and a synthesized model example projected into the image.

Human face is a surface lying in the 3-D space intrinsically. Therefore the 3-D model should be better for representing faces, especially to handle facial variations, such as pose, illumination etc. Blantz et al. proposed a method based on a 3-D morphable face model that encodes shape and texture in terms of model parameters, and algorithm that recovers these parameters from a single image of a face.

The main novelty of this approach is the ability to compare surfaces independent of natural deformations resulting from facial expressions. First, the range image and the texture of the face are acquired. Next, the range image is preprocessed by removing certain parts such as hair, which can complicate the recognition process.
Finally, a canonical form of the facial surface is computed. Such a representation is insensitive to head orientations and facial expressions, thus significantly simplifying the recognition procedure.
The recognition itself is performed on the canonical surfaces.

A probabilistic similarity measure based on Bayesian belief that the image intensity differences are characteristic of typical variations in appearance of an individual. Two classes of facial image variations are defined: intrapersonal variations and extrapersonal variations. Similarity among faces is measured using Bayesian rule.

Given a set of points belonging to two classes, a Support Vector Machine (SVM) finds the hyperplane that separates the largest possible fraction of points of the same class on the same side, while maximizing the distance from either class to the hyperplane. PCA is first used to extract features of face images and then discrimination functions between each pair of images are learned by SVMs.

Hidden Markov Models (HMM) are a set of statistical models used to characterize the statistical properties of a signal. HMM consists of two interrelated processes: (1) an underlying, unobservable Markov chain with a finite number of states, a state transition probability matrix and an initial state probability distribution and (2) a set of probability density functions associated with each state.

The idea behind Boosting is to sequentially employ a weak learner on a
weighted version of a given training sample set to generalize a set of
classifiers of its kind. Although any individual classifier may
perform slightly better than random guessing, the formed ensemble can
provide a very accurate (strong) classifier. Viola and Jones build the
first real-time face detection system by using AdaBoost, which is
considered a dramatic breakthrough in the face detection research. On the other hand, papers by Guo et al. are the first approaches on face recogntion using the AdaBoost methods.

During the last couple of years more and more research has been done in the area of face recognition from image sequences. Recognizing humans from real surveillance video is difficult because of the low quality of images and because face images are small. Still, a lot of improvement has been made.

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